The Intermodulation Coefficient of an Inhomogeneous Superconductor

TL;DR

This paper develops a theory linking inhomogeneity in high-T_c cuprate superconductors to their intermodulation properties, revealing that certain inhomogeneities can enhance critical supercurrent density, with implications for material performance.

Contribution

It introduces a formal analogy between inhomogeneous superconductors and nonlinear dielectrics, providing a new way to analyze and predict intermodulation effects in such materials.

Findings

Inhomogeneity can enhance the intermodulation critical supercurrent density J_{IMD}.

The continuum equations are equivalent to those of an inhomogeneous nonlinear dielectric.

Certain topologies of inhomogeneity lead to improved superconductor properties.

Abstract

The high-T_c cuprate superconductors are now believed to be intrinsically inhomogeneous. We develop a theory to describe how this inhomogeneity affects the intermodulation coefficient of such a material. We show that the continuum equations describing intermodulation in a superconducting layer with spatially varying properties are formally equivalent to those describing an inhomogeneous dielectric with a nonzero cubic nonlinearity. Using this formal analogy, we calculate the effect of inhomogeneity on the intermodulation coefficient in a high-T_c material, using several assumptions about the topology of the layer, and some simple analytical approximations to treat the nonlinearity. For some topologies, we find that the intermodulation critical supercurrent density J_{IMD} is actually enhanced compared to a homogeneous medium, thereby possibly leading to more desirable material properties. We discuss this result in light of recent spatial mappings of the superconducting energy gap in BSCCO-2212.